conservation laws

Conservation of linear momentum expresses the fact that a body or system of bodies in motion retains its total momentum, the product of mass and vector velocity, unless an external force is applied to it. In an isolated system (such as the universe), there are no external forces, so momentum is always conserved. Because momentum is conserved, its components in any direction will also be...

Hamilton’s equations

...on direction in space) and homogeneous (
H does not change with uniform translation in space), then Hamilton’s equations immediately yield the laws of conservation of angular momentum and linear momentum, respectively.